
%!TEX program = xelatex
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode

\documentclass[10pt]{article} 

\input{wang_preamble.tex}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{titling}
\setlength{\droptitle}{-2cm}   % This is your set screw

%%文档的题目、作者与日期
\author{UID \underline{\hspace{4cm}} \hspace{1cm} NAME \underline{\hspace{4cm}} }
\title{Mathematical Writing Exercise Chapter 3.14 - 3.38}
%\date{\vspace{-3ex}}
%\renewcommand{\today}{\number\year \,年 \number\month \,月 \number\day \,日}
%\date{2023 年 10 月 31 日}
\date{April 16, 2024}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{document}

\maketitle

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{enumerate}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\item  %Problem 01 ch3.14.7.  
True or False. (Distinctions: Which, That. )
\begin{enumerate}[label={(\arabic*)}]

%\item  Which, That. 

\item  A ``{\color{red}\it wicked which}'' (a term coined by Knuth [205]) is an instance of the word {\color{red}\it which} that should be {\color{red}\it that} (example: replace the word before {\color{red}\it should} earlier in this sentence by {\color{red}\it which}). 
The rule is that {\color{red}\it that} defines and restricts, whereas {\color{red}\it which} informs and does not restrict. 
%(Mathematicians should be good at spotting definitions.) 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  Note the difference between the following two examples. 
``Consider the Pei matrix, {\color{red}\it which} is positive definite.'' 
We are being told additional information about the Pei matrix: that it is positive definite.
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  ``Consider the Pei matrix {\color{red}\it that} is positive definite.'' 
Now we are being asked to focus on a particular Pei matrix from among several: the one that is positive definite. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  A useful guide is that {\color{red}\it which-clauses} are surrounded by commas, or preceded by a comma if at the end of a sentence. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  If you're not sure whether to use {\color{red}\it which} or {\color{red}\it that}, see whether your sentence looks right with commas around the relevant clause. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  An awkward ``that that'' is best avoided, even if it introduces a {\color{red}\it wicked which}, as has been done in the sentence ``This approach is similar to that {\color{red}\it which} we used in our earlier paper'' (though ``the one we used'' is better).
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  A rule of thumb discussed in [205, pp. 96-97] is to replace {\color{red}\it which} by {\color{red}\it that} whenever it sounds right to do so.
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\end{enumerate}

\vspace{0.2cm}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\item  %Problem 02 ch3.15.  
Fair or Better. (Double Negatives)
\begin{enumerate}[label={(\arabic*)}]

\item  A double negative is the use of two negative terms that cancel each other out to give the positive meaning. 
Double negatives are generally best avoided, as they make text harder to parse. 
%\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  
\begin{enumerate}
\item  ... but there is no reason why other visual aids should not be used. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)
\item  ... but other visual aids could be used.
\dotfill (\,\,\,\,\,\,\,\,\,\,)
\end{enumerate}

\item  
\begin{enumerate}
\item  The convergence of (1.1) is not guaranteed without additional assumptions on the function $g$ and the starting vector $x_0$. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)
\item  To guarantee convergence of (1.1) additional assumptions must be made on the function $g$ and the starting vector $x_0$.
\dotfill (\,\,\,\,\,\,\,\,\,\,)
\end{enumerate}

\item  
\begin{enumerate}
\item  If the input argument {\color{red}\texttt closure} is set to {\color{red}\texttt true}, all the dependencies are wrapped if they are not explicitly
marked as non-exportable. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)
\item  If the input argument {\color{red}\texttt closure} is set to {\color{red}\texttt true}, all the dependencies are wrapped unless they are explicitly marked as non-exportable. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)
\end{enumerate}

\item  
\begin{enumerate}
\item  It is not unreasonable to assume uniqueness of $x^*$. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)
\item  It is reasonable to assume uniqueness of $x^*$.
\dotfill (\,\,\,\,\,\,\,\,\,\,)
\end{enumerate}

\end{enumerate}


\vspace{0.2cm}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\item  %Problem 03 ch3.25.  
True or False. (Paragraphs)
\begin{enumerate}[label={(\arabic*)}]

\item  A standard device for making text more appealing is to break it into small paragraphs, as is done in newspapers. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  To communicate complex ideas in technical writing, short paragraphs are certainly helpful. ...... 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  {\color{red} Ideally, each paragraph contains a main idea or thought that separates it from its neighbors.} ...... 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  Long paragraphs tend to give a page a heavy look that can be a visual deterrent to the potential reader. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  A long paragraph that is hard to break may be indicative of convoluted thinking. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  A mix of different lengths is best. The best writers occasionally slip in one-sentence paragraphs.
\dotfill (\,\,\,\,\,\,\,\,\,\,)


\end{enumerate}


\vspace{0.2cm}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\item  %Problem 04 ch 3.26. 
True or False. (Punctuation - 1)
\begin{enumerate}[label={(\arabic*)}]

\item  Much can be said about punctuation, and for thorough treatments of the topic I refer the reader to the references mentioned in Chapter 4. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  It is worth keeping in mind G. V. Carey's explanation [62] that ``the main function of punctuation is {\color{red}\it to make perfectly clear the construction} of the written words''.  
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  A few common mistakes and difficulties deserve mention here.
%\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item   In ``This result is well known, see [9]'' the {\color{red}comma} should be a {\color{red} semicolon}, which conveys a slightly longer pause. 
Even better is to say ``This result is well known [9]''.  
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  A common mistake is the let-comma-then construction: ``Let $x^*$ be a local maximum of $F(x)$, then a Taylor series expansion gives ... '' The comma should be a {\color{red} period}. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  Similarly, the comma should be a semicolon, or even a period, in ``This bound has the disadvantage that it uses a norm of $X$, moreover the multiplicative constant can be large when $X$ is not a normal matrix''.  
These errors are called ``{\color{red}\it comma splices}'' by Karen Gordon [121]. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item   In this sentence the semicolon should be a comma: ``The secant method can also be used; its lack of need for derivatives being an advantage''.  
A rough guide is to use a semicolon only where you could also use a period.
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item   In the sentence ``If we use iterative refinement solutions are computed to higher accuracy,'' a comma is needed after ``refinement'', otherwise the reader may take ``iterative refinement'' as modifying ``solutions''. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  Another example where a comma is needed to avoid a possible misread is the sentence ``However, the singularity can be removed by a change of variable.''
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\end{enumerate}


\vspace{0.2cm}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\item  %Problem 05 ch 3.26. 
True or False. (Punctuation - 2 )
\begin{enumerate}[label={(\arabic*)}]


\item  {\color{red} The exclamation mark} should be used with extreme caution in technical writing. 
If you are tempted to exclaim, read ``!'' as ``shriek''; nine times out of ten you will decide a period is adequate. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  An example of correct usage is, from Parlett [257, p. 46]: ``When $A$ is tridiagonal the computation of $A^{-1}u$ costs little more than the computation of $Au$!'' 
The exclamation mark could be omitted, but then the reader might not realize that this is a surprising fact. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  Another example, from Knuth [201, p. 45], is ``The chi-square table tells us, in fact, that $V_2$ {\color{red}\it is much too low}: the observed values are so close to the expected values, we cannot consider the result to be random!'' 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  In the United States, standard practice is to surround quotes by {\color{red}double quotation marks}, with {\color{red}single quotation marks} being used for a quote within a quote. 
In the United Kingdom, the reverse practice is generally used. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  The placement of final punctuation marks also differs: in US usage, the final punctuation is placed inside the {\color{red}closing quotation marks} (except for ``!'' and ``?'' when they are not part of the quotation), while in UK usage it goes outside (except for ``!'' and ``?'' when they are part of the quotation).
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  {\color{red} An apostrophe} denotes possession for nouns (the proof's length) but not for pronouns (this book is yours). 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  An apostrophe is used with the plural of letters and of words when the words are used without regard to their meaning: ``there are three l's in the word parallel,'' ``his prose contains too many however's.'' 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  For {\color{red} plurals} of numbers the apostrophe can be omitted: ``a random matrix of 0s and 1s.'' 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  For plurals of mathematical symbols or expressions the apostrophe will usually be needed to avoid ambiguity: 
``these $f$'s are all continuous,'' ``likewise for the $Z_k$'s,'' ``these $\delta$'s are all of order $10^{-8}$. '' 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\end{enumerate}

\vspace{0.2cm}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\item  %Problem 06 ch 3.35. 
True or False. (Split Infinitives)
\begin{enumerate}[label={(\arabic*)}]

\item  A split infinitive is a phrase of the from ``to-adverb-verb.'' 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  Splitting {\color{red}\it to} from the corresponding verb is considered by some to be bad grammar, though there is no real basis for this belief and the practice is widely accepted.
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  Perhaps the most famous split infinitive is Star Trek's ``{\color{red} to boldly go where no man has gone before.}'' 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  {\color{red}It is worth trying to rewrite a sentence to avoid a split infinitive,} but as Bernstein advises [32, p. 425], it ``is unwise to appear to be going out of one's way'' to avoid one. 
Here are two examples.
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  Original: \TeX's line breaking algorithm tries {\color{red}to not hyphenate} the second-last line of a paragraph.
Better: \TeX's line breaking algorithm tries {\color{red}not to hyphenate} the second-last line of a paragraph.
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  Original: The aim of this section is {\color{red}to clearly show} the superiority of the new method. 
Better: The aim of this section is {\color{red}to show clearly} the superiority of the new method. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  But in the sentence ``The effect of removing that line from the code is {\color{red}to almost double} the execution time.'' rewriting as "almost to double" sounds unnatural, so the sentence is best left as is. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  In a split infinitive the verb must be in the infinitive form, so ``to have greatly exceeded,'' for example, is not a split infinitive.
\dotfill (\,\,\,\,\,\,\,\,\,\,)


\end{enumerate}

\vspace{0.2cm}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\item  %Problem 07 ch 3.36. 
True or False. (Synonym Selection)
\begin{enumerate}[label={(\arabic*)}]

\item  English is one of the most synonym-rich languages, thanks to the words it has adopted from other languages, and {\color{red}each member of a set of synonyms can have a different tone and shade of meaning. }
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  A dictionary and a thesaurus are vital aids to choosing the right word. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  When you have a choice of words, {\color{red}use a short, concrete one} in preference to a long or abstract one. 
Often, this means using an Anglo-Saxon word instead of one of French or Latin origin, as the table illustrates. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\begin{table}[ht!]
\centering
\caption{The origins of some synonyms.\vspace{0.3cm}}
\begin{tabular}{lll}\hline 
Anglo-Saxon & French & Latin \\ \hline \hline 
ask & question & interrogate \\ \hline 
rise & mount & ascend \\ \hline 
good & marvelous & superior \\ \hline 
show & establish & exhibit, demonstrate \\ \hline 
need & requirement & necessity \\ \hline 
think & ponder & cogitate \\ \hline 
\end{tabular}
\end{table}

\item  Don't be afraid of using a long or unusual word if it is just the right one, or if it adds spice to your writing or conveys an interesting image. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  Forman Acton [2, p. 145] writes ``The second term ... is {\color{red}obstreperous}.'' 
No other word quite so vividly describes the uncontrollable term to which he refers (with the possible exception of {\color{red}\it recalcitrant}, another word used by Acton in the same book).
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  It helps to think of word pyramids showing levels of abstraction [334], such as the one in Figure 3.1. 
As Turk and Kirkman [333] point out, ``{\color{red}Abstract words are less easy to decode} because the reader has to `scan' all the possibilities subconsciously before deciding on a specific meaning.''
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  Generally, it is best to use the least abstract, most specific word possible.
This leads to more lively and precise prose. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

%\item  Here are some examples of chains of words in order of increasing specificity. 
%\dotfill (\,\,\,\,\,\,\,\,\,\,)


\end{enumerate}


\vspace{0.2cm}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\item  %Problem 08 ch 3.37. 
True or False. (Tenses)
\begin{enumerate}[label={(\arabic*)}]

\item  One of the decisions the writer of a technical paper must make is what tense to use. 
There are no hard and fast rules, except to be consistent in the use of tense, but I offer some guidelines. ......
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  {\color{red} I prefer the present tense to the future tense for referring to later parts of the paper.} Thus I write ``This is proved in Theorem 3, below'' rather than ``This will be proved in Theorem 3,'' and ``We discuss these matters in detail in Section 5'' rather than ``We will discuss these matters in detail.'' 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  Note that since the latter example does not contain a section reference it could be construed as referring to a future paper; this potential ambiguity is a danger of using the future tense. ......
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  {\color{red} The present tense can also be used for backward references,} as in ``The analysis of Section 1 proves the following,'' {\color{red} though the past tense is more common:} ``We showed/saw in Section 1 that.'' 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  Tables and figures exist in the present, so the present tense should be used to refer to them: ``Table 4 shows that,'' ``Figure 1 displays.'' 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  Similarly, in a citation where the reference is the subject of the sentence, the present tense is the one to use: ``Reference [4] contains the interesting result that.'' 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  To refer to work in earlier papers either the past or the present tense can be used: ``Banach shows that'' or ``Banach showed that.'' 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  I use the present tense unless I want to emphasize the historical aspects of the reference, as, for example, when summarizing a number of earlier results in a survey. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  {\color{red} A summary or conclusions section should use the past tense when specifying actions:} ``We have shown that'' or ``We showed that'' rather than ``We show that.'' 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  {\color{red} If a simple statement of results is given, however, the present tense is appropriate:} ``Asymptotic expansions are useful for ...'', ``Our conclusion is that ...''. 
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\end{enumerate}

\vspace{0.2cm}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\item  %Problem 09 ch 3.38. 
Rewrite. (The Ten Commandments of Good Writing)
\begin{enumerate}[label={(\arabic*)}]

\item  Each pronoun should agree with their antecedent.
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  Just between you and I, case is important.
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  A preposition is a poor word to end a sentence with.
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  Verbs has to agree with their subject.
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  Don't use no double negatives.
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  Remember to never split an infinitive.
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  When dangling, don't use participles.
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  Join clauses good, like a conjunction should.
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  Don't write a run-on sentence it is difficult when you got to punctuate it so it makes sense when the reader reads what you wrote.
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\item  About sentence fragments.
\dotfill (\,\,\,\,\,\,\,\,\,\,)

\end{enumerate}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\end{enumerate}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\end{document}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


